Fluorescence imaging opens new possibilities for intraoperative guidance and early cancer detection, in particular when using agents that target specific disease features. Nevertheless, photon scattering in tissue degrades image quality and leads to ambiguity in fluorescence image interpretation and challenges clinical translation. We introduce the concept of capturing the spatially-dependent impulse response of an image and investigate Spatially Adaptive Impulse Response Correction (SAIRC), a method that is proposed for improving the accuracy and sensitivity achieved. Unlike classical methods that presume a homogeneous spatial distribution of optical properties in tissue, SAIRC explicitly measures the optical heterogeneity in tissues. This information allows, for the first time, the application of spatially-dependent deconvolution to correct the fluorescence images captured in relation to their modification by photon scatter. Using experimental measurements from phantoms and animals, we investigate the improvement in resolution and quantification over non-corrected images. We discuss how the proposed method is essential for maximizing the performance of fluorescence molecular imaging in the clinic.